where the integral appearing has been evaluated in [1]}, and it takes the form (keeping only the non-analytic term):
\(I_{\mathcal {B}}\ =\ \lim _{d\rightarrow 3 } \int \frac{d^{d}\mathbf {k}}{(2\pi )^{d}}\frac{1}{(\mathbf {p}+\mathbf {k})^2(\mathbf {p}^{^{\prime }}+\mathbf {k})^2(\mathbf {p}^2-\mathbf {k}^2)} \ = \ \frac{i }{8 \pi \vert \mathbf {p}\vert \ \mathbf {q}^2}\log (\mathbf {q}^2) +\ldots \ .\) 
